Moving multiple vertices in a model
The original object can have a Shrink Wrap Modifier added. Later you may choose to press the Apply Button or Apply as Shape Key.


Objects and Outliner above.



Original yellow object with Shrink Wrap Modifier not visible in 3D View in the image above.



Original yellow object with Shrink Wrap Modifier visible 3D View in the view above.


The vertex group selected in the image above.



The target of the shrink wrap.  Cube Scaled on X axis in edit mode with Mirror Modifier and Empty placed at center.  You can be more artistic.